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SIGNATURE-BASED INFORMATION MEASURES OF MULTI-STATE NETWORKS

Published online by Cambridge University Press:  14 June 2018

S. Zarezadeh ,
M. Asadi  and
S. Eftekhar
S. Zarezadeh
Affiliation:
Department of Statistics, Shiraz University, Shiraz 71454, Iran E-mail: s.zarezadeh@shirazu.ac.ir
M. Asadi
Affiliation:
Department of Statistics, University of Isfahan, Isfahan 81744, Iranand School of Mathematics, Institute of Research in Fundamental Sciences (IPM), P.O Box 19395-5746, Tehran, Iran E-mail: m.assadi@sci.ui.ac.ir
S. Eftekhar
Affiliation:
Department of Statistics, Shiraz University, Shiraz 71454, Iran E-mail: sana.eftekhar@shirazu.ac.ir
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Abstract

The signature matrix of an n-component three-state network (system), which depends only on the network structure, is a useful tool for comparing the reliability and stochastic properties of networks. In this paper, we consider a three-state network with states up, partial performance, and down. We assume that the network remains in state up, for a random time T1 and then moves to state partial performance until it fails at time T>T1. The signature-based expressions for the conditional entropy of T given T1, the joint entropy, Kullback-Leibler (K-L) information, and mutual information of the lifetimes T and T1 are presented. It is shown that the K-L information, and mutual information between T1 and T depend only on the network structure (i.e., depend only to the signature matrix of the network). Some signature-based stochastic comparisons are also made to compare the K-L of the state lifetimes in two different three-state networks. Upper and lower bounds for the K-L divergence and mutual information between T1 and T are investigated. Finally the results are extended to n-component multi-state networks. Several examples are examined graphically and numerically.

Keywords

joint entropyKullback–Liebler informationmutual informationorder statisticssignatureShannon entropy
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 3 , July 2019 , pp. 438 - 459
Copyright
Copyright © Cambridge University Press 2018 

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